Which of following statements is incorrect?

Options

A. Path length is a scalr quantity whereas displacement is a vector quantity
B. The magnitude of displacement is always equal to the path length traversed by an object over a given time interval
C. The displacement depends only on the end points whereas path length depends on the actual path followed.
D. The path length is always positive whereas displacement can be possitive, negative and zero.

Answer

To solve the question of which statement is incorrect regarding path length and displacement, we will analyze each option one by one.

### Step 1: Analyze Option 1
**Statement:** "Path length is a scalar quantity while displacement is a vector quantity."

**Explanation:**
- Path length refers to the total distance traveled by an object, regardless of direction. It only has magnitude and is therefore a scalar quantity.
- Displacement, on the other hand, is defined as the change in position of an object and has both magnitude and direction, making it a vector quantity.

**Conclusion:** This statement is **correct**.

### Step 2: Analyze Option 2
**Statement:** "The magnitude of displacement is always equal to the path length traveled by the object over a time interval."

**Explanation:**
- Displacement can be less than or equal to the path length. In cases where an object moves in a straight line without changing direction, the displacement can equal the path length. However, if the object takes a curved or indirect path, the displacement will be less than the path length.
- Therefore, it is incorrect to say that the magnitude of displacement is always equal to the path length.

**Conclusion:** This statement is **incorrect**.

### Step 3: Analyze Option 3
**Statement:** "Displacement depends only upon the end points whereas the path length depends upon the actual path."

**Explanation:**
- Displacement is calculated based on the initial and final positions (end points) of the object, regardless of the path taken.
- Path length, however, is the total distance traveled along the actual path taken by the object.

**Conclusion:** This statement is **correct**.

### Step 4: Analyze Option 4
**Statement:** "Path length is always positive whereas displacement can be positive, negative, as well as zero."

**Explanation:**
- Path length, being a measure of distance, is always a positive value.
- Displacement can be positive (when the final position is ahead of the initial position), negative (when the final position is behind the initial position), or zero (when the initial and final positions are the same).

**Conclusion:** This statement is **correct**.

### Final Conclusion
After analyzing all the statements, we find that the incorrect statement is **Option 2**: "The magnitude of displacement is always equal to the path length traveled by the object over a time interval."

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